nag_opt_handle_solve_lp_ipm (e04mtc) Example Program Results
++++++++++ Use the Primal-Dual algorithm ++++++++++
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E04MT, Interior point method for LP problems
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Begin of Options
Print File = 6 * d
Print Level = 2 * d
Print Options = Yes * d
Print Solution = All * U
Monitoring File = -1 * d
Monitoring Level = 4 * d
Lpipm Monitor Frequency = 1 * U
Infinite Bound Size = 1.00000E+20 * d
Task = Minimize * d
Stats Time = No * d
Lp Presolve = Yes * d
Lpipm Algorithm = Primal-dual * d
Lpipm Centrality Correctors = -6 * U
Lpipm Iteration Limit = 100 * d
Lpipm Max Iterative Refinement= 5 * d
Lpipm Scaling = Arithmetic * d
Lpipm Stop Tolerance = 1.00000E-10 * U
Lpipm Stop Tolerance 2 = 2.67452E-10 * d
Lpipm System Formulation = Auto * d
End of Options
Problem Statistics
No of variables 7
free (unconstrained) 0
bounded 7
No of lin. constraints 7
nonzeroes 41
Objective function Linear
Presolved Problem Measures
No of variables 13
free (unconstrained) 0
No of lin. constraints 7
nonzeroes 47
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it| pobj | dobj | optim | feas | compl | mu | mcc | I
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0 -7.86591E-02 1.71637E-02 1.27E+00 1.06E+00 8.89E-02 1.5E-01
1 5.74135E-03 -2.24369E-02 6.11E-16 1.75E-01 2.25E-02 2.8E-02 0
2 1.96803E-02 1.37067E-02 5.06E-16 2.28E-02 2.91E-03 3.4E-03 0
3 2.15232E-02 1.96162E-02 7.00E-15 9.24E-03 1.44E-03 1.7E-03 0
4 2.30321E-02 2.28676E-02 1.15E-15 2.21E-03 2.97E-04 3.4E-04 0
5 2.35658E-02 2.35803E-02 1.32E-15 1.02E-04 8.41E-06 9.6E-06 0
6 2.35965E-02 2.35965E-02 1.64E-15 7.02E-08 6.35E-09 7.2E-09 0
Iteration 7
monit() reports good approximate solution (tol =, 1.20e-08):
7 2.35965E-02 2.35965E-02 1.35E-15 3.52E-11 3.18E-12 3.6E-12 0
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Status: converged, an optimal solution found
------------------------------------------------------------------------------
Final primal objective value 2.359648E-02
Final dual objective value 2.359648E-02
Absolute primal infeasibility 4.168797E-15
Relative primal infeasibility 1.350467E-15
Absolute dual infeasibility 5.084353E-11
Relative dual infeasibility 3.518607E-11
Absolute complementarity gap 2.685778E-11
Relative complementarity gap 3.175366E-12
Iterations 7
Primal variables:
idx Lower bound Value Upper bound
1 -1.00000E-02 -1.00000E-02 1.00000E-02
2 -1.00000E-01 -1.00000E-01 1.50000E-01
3 -1.00000E-02 3.00000E-02 3.00000E-02
4 -4.00000E-02 2.00000E-02 2.00000E-02
5 -1.00000E-01 -6.74853E-02 5.00000E-02
6 -1.00000E-02 -2.28013E-03 inf
7 -1.00000E-02 -2.34528E-04 inf
Box bounds dual variables:
idx Lower bound Value Upper bound Value
1 -1.00000E-02 3.30098E-01 1.00000E-02 0.00000E+00
2 -1.00000E-01 1.43844E-02 1.50000E-01 0.00000E+00
3 -1.00000E-02 0.00000E+00 3.00000E-02 9.09967E-02
4 -4.00000E-02 0.00000E+00 2.00000E-02 7.66124E-02
5 -1.00000E-01 3.51391E-11 5.00000E-02 0.00000E+00
6 -1.00000E-02 3.42902E-11 inf 0.00000E+00
7 -1.00000E-02 8.61040E-12 inf 0.00000E+00
Linear constraints dual variables:
idx Lower bound Value Upper bound Value
1 -1.30000E-01 0.00000E+00 -1.30000E-01 1.43111E+00
2 -inf 0.00000E+00 -4.90000E-03 4.00339E-10
3 -inf 0.00000E+00 -6.40000E-03 1.54305E-08
4 -inf 0.00000E+00 -3.70000E-03 3.80136E-10
5 -inf 0.00000E+00 -1.20000E-03 4.72629E-11
6 -9.92000E-02 1.50098E+00 inf 0.00000E+00
7 -3.00000E-03 1.51661E+00 2.00000E-03 0.00000E+00
++++++++++ Use the Self-Dual algorithm ++++++++++
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E04MT, Interior point method for LP problems
----------------------------------------------
Begin of Options
Print File = 6 * d
Print Level = 2 * d
Print Options = Yes * d
Print Solution = All * U
Monitoring File = -1 * d
Monitoring Level = 4 * d
Lpipm Monitor Frequency = 1 * U
Infinite Bound Size = 1.00000E+20 * d
Task = Minimize * d
Stats Time = No * d
Lp Presolve = Yes * d
Lpipm Algorithm = Self-dual * U
Lpipm Centrality Correctors = -6 * U
Lpipm Iteration Limit = 100 * d
Lpipm Max Iterative Refinement= 5 * d
Lpipm Scaling = Arithmetic * d
Lpipm Stop Tolerance = 1.00000E-10 * U
Lpipm Stop Tolerance 2 = 1.00000E-11 * U
Lpipm System Formulation = Auto * d
End of Options
Problem Statistics
No of variables 7
free (unconstrained) 0
bounded 7
No of lin. constraints 7
nonzeroes 41
Objective function Linear
Presolved Problem Measures
No of variables 13
free (unconstrained) 0
No of lin. constraints 7
nonzeroes 47
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it| pobj | dobj | p.inf | d.inf | d.gap | tau | mcc | I
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0 -6.39941E-01 4.94000E-02 1.07E+01 2.69E+00 5.54E+00 1.0E+00
1 -8.56025E-02 -1.26938E-02 2.07E-01 2.07E-01 2.07E-01 1.7E+00 0
2 4.09196E-03 1.24373E-02 4.00E-02 4.00E-02 4.00E-02 2.8E+00 0
3 1.92404E-02 2.03658E-02 6.64E-03 6.64E-03 6.64E-03 3.2E+00 1
4 1.99631E-02 2.07574E-02 3.23E-03 3.23E-03 3.23E-03 2.3E+00 1
5 2.03834E-02 2.11141E-02 1.68E-03 1.68E-03 1.68E-03 1.4E+00 0
6 2.22419E-02 2.25057E-02 5.73E-04 5.73E-04 5.73E-04 1.4E+00 1
7 2.35051E-02 2.35294E-02 6.58E-05 6.58E-05 6.58E-05 1.4E+00 6
8 2.35936E-02 2.35941E-02 1.19E-06 1.19E-06 1.19E-06 1.4E+00 0
Iteration 9
monit() reports good approximate solution (tol =, 1.20e-08):
9 2.35965E-02 2.35965E-02 5.37E-10 5.37E-10 5.37E-10 1.4E+00 0
Iteration 10
monit() reports good approximate solution (tol =, 1.20e-08):
10 2.35965E-02 2.35965E-02 2.68E-13 2.68E-13 2.68E-13 1.4E+00 0
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Status: converged, an optimal solution found
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Final primal objective value 2.359648E-02
Final dual objective value 2.359648E-02
Absolute primal infeasibility 2.853383E-12
Relative primal infeasibility 2.677658E-13
Absolute dual infeasibility 1.485749E-12
Relative dual infeasibility 2.679654E-13
Absolute complementarity gap 7.228861E-13
Relative complementarity gap 2.683908E-13
Iterations 10
Primal variables:
idx Lower bound Value Upper bound
1 -1.00000E-02 -1.00000E-02 1.00000E-02
2 -1.00000E-01 -1.00000E-01 1.50000E-01
3 -1.00000E-02 3.00000E-02 3.00000E-02
4 -4.00000E-02 2.00000E-02 2.00000E-02
5 -1.00000E-01 -6.74853E-02 5.00000E-02
6 -1.00000E-02 -2.28013E-03 inf
7 -1.00000E-02 -2.34528E-04 inf
Box bounds dual variables:
idx Lower bound Value Upper bound Value
1 -1.00000E-02 3.30098E-01 1.00000E-02 0.00000E+00
2 -1.00000E-01 1.43844E-02 1.50000E-01 0.00000E+00
3 -1.00000E-02 0.00000E+00 3.00000E-02 9.09967E-02
4 -4.00000E-02 0.00000E+00 2.00000E-02 7.66124E-02
5 -1.00000E-01 3.66960E-12 5.00000E-02 0.00000E+00
6 -1.00000E-02 2.47652E-11 inf 0.00000E+00
7 -1.00000E-02 7.82645E-13 inf 0.00000E+00
Linear constraints dual variables:
idx Lower bound Value Upper bound Value
1 -1.30000E-01 0.00000E+00 -1.30000E-01 1.43111E+00
2 -inf 0.00000E+00 -4.90000E-03 1.07904E-10
3 -inf 0.00000E+00 -6.40000E-03 1.14799E-09
4 -inf 0.00000E+00 -3.70000E-03 4.09190E-12
5 -inf 0.00000E+00 -1.20000E-03 1.52421E-12
6 -9.92000E-02 1.50098E+00 inf 0.00000E+00
7 -3.00000E-03 1.51661E+00 2.00000E-03 0.00000E+00